Projet Régression 2017
Jean-Baptiste AUJOGUE jean-baptiste.aujogue@etu.univ-lyon1.fr, Xian YANG xian.yang@etu.univ-lyon1.fr
24 déc. 2017
set.seed(11715490)Pour lire fichiers en format .arff
## install.packages("foreign")
library(foreign)
setwd("C:/Users/ellie/Documents/R/OpticalBurstSwitching")
OBS <- read.arff("OBS-Network-DataSet_2_Aug27.arff")
head(OBS)## Node Utilised Bandwith Rate Packet Drop Rate Full_Bandwidth
## 1 3 0.822038 0.190381 1000
## 2 9 0.275513 0.729111 100
## 3 3 0.923707 0.090383 900
## 4 9 0.368775 0.637710 100
## 5 3 0.905217 0.108670 800
## 6 9 0.514687 0.494142 100
## Average_Delay_Time_Per_Sec Percentage_Of_Lost_Pcaket_Rate
## 1 0.004815 19.031487
## 2 0.004815 72.889036
## 3 0.000633 9.035834
## 4 0.000552 63.737843
## 5 0.000497 10.864208
## 6 0.003098 49.392131
## Percentage_Of_Lost_Byte_Rate Packet Received Rate of Used_Bandwidth
## 1 19.038129 0.809619 822.03750
## 2 72.911141 0.270889 27.55125
## 3 9.038339 0.909617 831.33600
## 4 63.770999 0.362290 36.87750
## 5 10.866977 0.891330 724.17375
## 6 49.414235 0.505858 51.46875
## Lost_Bandwidth Packet Size_Byte Packet_Transmitted Packet_Received
## 1 177.96250 1440 90324 73128
## 2 72.44875 1440 9048 2451
## 3 68.66400 1440 81276 73930
## 4 63.12250 1440 9048 3278
## 5 75.82625 1440 72228 64379
## 6 48.53125 1440 9048 4577
## Packet_lost Transmitted_Byte Received_Byte 10-Run-AVG-Drop-Rate
## 1 17196 130066560 105304320 0.146594
## 2 6598 13029120 3529440 0.517669
## 3 7346 117037440 106459200 0.058749
## 4 5770 13029120 4720320 0.522922
## 5 7849 104008320 92705760 0.076069
## 6 4471 13029120 6590880 0.405197
## 10-Run-AVG-Bandwith-Use 10-Run-Delay Node Status Flood Status
## 1 0.780936 0.001838 B 0.023455
## 2 0.242451 0.002236 NB 0.460725
## 3 0.886758 0.001751 B 0.000000
## 4 0.324522 0.001776 NB 0.439255
## 5 0.869009 0.001767 B 0.000000
## 6 0.442631 0.002250 NB 0.291742
## Class
## 1 NB-No Block
## 2 Block
## 3 No Block
## 4 Block
## 5 No Block
## 6 NB-No Blockdim(OBS)## [1] 1075 22summary(OBS) # On voit que la variable `Packet Size_Byte` est complètement inutile car elle ne change jamais (=1440). On va la virer.## Node Utilised Bandwith Rate Packet Drop Rate Full_Bandwidth
## Min. :3.000 Min. :0.2356 Min. :0.08613 Min. : 100.0
## 1st Qu.:3.000 1st Qu.:0.4469 1st Qu.:0.24754 1st Qu.: 300.0
## Median :9.000 Median :0.5772 Median :0.43799 Median : 500.0
## Mean :6.014 Mean :0.5979 Mean :0.41136 Mean : 540.5
## 3rd Qu.:9.000 3rd Qu.:0.7645 3rd Qu.:0.55658 3rd Qu.: 800.0
## Max. :9.000 Max. :0.9280 Max. :0.76794 Max. :1000.0
##
## Average_Delay_Time_Per_Sec Percentage_Of_Lost_Pcaket_Rate
## Min. :0.0004060 Min. : 8.61
## 1st Qu.:0.0004510 1st Qu.:24.75
## Median :0.0006110 Median :43.80
## Mean :0.0009619 Mean :41.16
## 3rd Qu.:0.0009530 3rd Qu.:56.67
## Max. :0.0052370 Max. :76.79
##
## Percentage_Of_Lost_Byte_Rate Packet Received Rate of Used_Bandwidth
## Min. : 8.613 Min. :0.2321 Min. : 27.55
## 1st Qu.:24.754 1st Qu.:0.4333 1st Qu.:138.41
## Median :43.799 Median :0.5620 Median :291.59
## Mean :41.192 Mean :0.5881 Mean :340.78
## 3rd Qu.:56.672 3rd Qu.:0.7525 3rd Qu.:515.18
## Max. :76.794 Max. :0.9139 Max. :867.04
##
## Lost_Bandwidth Packet Size_Byte Packet_Transmitted Packet_Received
## Min. : 34.16 Min. :1440 Min. : 9048 Min. : 2451
## 1st Qu.: 81.20 1st Qu.:1440 1st Qu.:27092 1st Qu.:12491
## Median :159.51 Median :1440 Median :45188 Median :26847
## Mean :199.68 Mean :1440 Mean :48826 Mean :30593
## 3rd Qu.:279.27 3rd Qu.:1440 3rd Qu.:72228 3rd Qu.:46588
## Max. :687.93 Max. :1440 Max. :90324 Max. :77131
##
## Packet_lost Transmitted_Byte Received_Byte
## Min. : 3913 Min. : 13029120 Min. : 3529440
## 1st Qu.: 7984 1st Qu.: 39012480 1st Qu.: 17736480
## Median :14944 Median : 65070720 Median : 37357920
## Mean :18590 Mean : 70308837 Mean : 49873429
## 3rd Qu.:25962 3rd Qu.:104008320 3rd Qu.: 67086720
## Max. :62415 Max. :130066560 Max. :980066560
## NA's :15
## 10-Run-AVG-Drop-Rate 10-Run-AVG-Bandwith-Use 10-Run-Delay
## Min. :0.05875 Min. :0.2074 Min. :0.0004050
## 1st Qu.:0.18993 1st Qu.:0.3799 1st Qu.:0.0006560
## Median :0.30702 Median :0.5089 Median :0.0007650
## Mean :0.30760 Mean :0.5532 Mean :0.0009336
## 3rd Qu.:0.40600 3rd Qu.:0.7341 3rd Qu.:0.0009840
## Max. :0.63371 Max. :0.8909 Max. :0.0049040
##
## Node Status Flood Status Class
## B :475 Min. :0.00000 Block :120
## NB :285 1st Qu.:0.02305 NB-No Block:500
## P NB:315 Median :0.07933 NB-Wait :300
## Mean :0.13194 No Block :155
## 3rd Qu.:0.23054
## Max. :0.56674
## OBS <- OBS[names(OBS) != "Packet Size_Byte"]
names(OBS)## [1] "Node" "Utilised Bandwith Rate"
## [3] "Packet Drop Rate" "Full_Bandwidth"
## [5] "Average_Delay_Time_Per_Sec" "Percentage_Of_Lost_Pcaket_Rate"
## [7] "Percentage_Of_Lost_Byte_Rate" "Packet Received Rate"
## [9] "of Used_Bandwidth" "Lost_Bandwidth"
## [11] "Packet_Transmitted" "Packet_Received"
## [13] "Packet_lost" "Transmitted_Byte"
## [15] "Received_Byte" "10-Run-AVG-Drop-Rate"
## [17] "10-Run-AVG-Bandwith-Use" "10-Run-Delay"
## [19] "Node Status" "Flood Status"
## [21] "Class"names(OBS) <- make.names(names(OBS), unique = TRUE)Traitement des valeurs manquantes
valMan <- which(is.na(OBS), arr.ind = TRUE, useNames = TRUE)
dim(valMan) # Only 15 * 2 so we don't have to draw it.## [1] 15 2library(mice)
mdp <- md.pattern(OBS)
mdp## Node Utilised.Bandwith.Rate Packet.Drop.Rate Full_Bandwidth
## 1060 1 1 1 1
## 15 1 1 1 1
## 0 0 0 0
## Average_Delay_Time_Per_Sec Percentage_Of_Lost_Pcaket_Rate
## 1060 1 1
## 15 1 1
## 0 0
## Percentage_Of_Lost_Byte_Rate Packet.Received..Rate of.Used_Bandwidth
## 1060 1 1 1
## 15 1 1 1
## 0 0 0
## Lost_Bandwidth Packet_Transmitted Packet_Received Transmitted_Byte
## 1060 1 1 1 1
## 15 1 1 1 1
## 0 0 0 0
## Received_Byte X10.Run.AVG.Drop.Rate X10.Run.AVG.Bandwith.Use
## 1060 1 1 1
## 15 1 1 1
## 0 0 0
## X10.Run.Delay Node.Status Flood.Status Class Packet_lost
## 1060 1 1 1 1 1 0
## 15 1 1 1 1 0 1
## 0 0 0 0 15 15library(ipred)
# preproc <- preProcess(OBS, method = "bagImpute")
# mice(OBS, m=5, maxit=50, meth='pmm', seed=500)
# OBScomplet <- mice(OBS)
# aggr(mdp, prop = FALSE, numbers = TRUE)
# install.packages("DMwR")
library(DMwR)## Warning: package 'DMwR' was built under R version 3.4.3## Loading required package: lattice## Loading required package: gridOBScomplet <- knnImputation(OBS[! names(OBS) %in% c("Node.Status", "Class")])
OBScomplet[valMan]## [1] 20480.07 12191.96 11870.21 20480.07 12191.96 11870.21 20480.07
## [8] 12191.96 11870.21 20480.07 12191.96 11870.21 20480.07 12191.96
## [15] 11870.21head(OBScomplet) ## Node Utilised.Bandwith.Rate Packet.Drop.Rate Full_Bandwidth
## 1 3 0.822038 0.190381 1000
## 2 9 0.275513 0.729111 100
## 3 3 0.923707 0.090383 900
## 4 9 0.368775 0.637710 100
## 5 3 0.905217 0.108670 800
## 6 9 0.514687 0.494142 100
## Average_Delay_Time_Per_Sec Percentage_Of_Lost_Pcaket_Rate
## 1 0.004815 19.031487
## 2 0.004815 72.889036
## 3 0.000633 9.035834
## 4 0.000552 63.737843
## 5 0.000497 10.864208
## 6 0.003098 49.392131
## Percentage_Of_Lost_Byte_Rate Packet.Received..Rate of.Used_Bandwidth
## 1 19.038129 0.809619 822.03750
## 2 72.911141 0.270889 27.55125
## 3 9.038339 0.909617 831.33600
## 4 63.770999 0.362290 36.87750
## 5 10.866977 0.891330 724.17375
## 6 49.414235 0.505858 51.46875
## Lost_Bandwidth Packet_Transmitted Packet_Received Packet_lost
## 1 177.96250 90324 73128 17196
## 2 72.44875 9048 2451 6598
## 3 68.66400 81276 73930 7346
## 4 63.12250 9048 3278 5770
## 5 75.82625 72228 64379 7849
## 6 48.53125 9048 4577 4471
## Transmitted_Byte Received_Byte X10.Run.AVG.Drop.Rate
## 1 130066560 105304320 0.146594
## 2 13029120 3529440 0.517669
## 3 117037440 106459200 0.058749
## 4 13029120 4720320 0.522922
## 5 104008320 92705760 0.076069
## 6 13029120 6590880 0.405197
## X10.Run.AVG.Bandwith.Use X10.Run.Delay Flood.Status
## 1 0.780936 0.001838 0.023455
## 2 0.242451 0.002236 0.460725
## 3 0.886758 0.001751 0.000000
## 4 0.324522 0.001776 0.439255
## 5 0.869009 0.001767 0.000000
## 6 0.442631 0.002250 0.291742# install.packages("Amelia")
# library(Amelia)
# missmap(OBS)Méthode ACP
library(plotly)## Loading required package: ggplot2##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutcorOBS <- cor(OBScomplet[! names(OBScomplet) %in% c("Node.Status", "Class")])
corHmp <- plot_ly(x = names(OBScomplet[! names(OBScomplet) %in% c("Node.Status", "Class")]),
y = names(OBScomplet[! names(OBScomplet) %in% c("Node.Status", "Class")]), z = corOBS, type = "heatmap")
corHmpIn the correlation heatmap we can repeatly spot extremely high pairwise correlation close or even equal to 1 or -1. Highly to perfectly correlated variables could bias the PCA result in a way that PCA will overemphasize the common contribution of the (nearly) redundant variables. Therefore, it might make sense to find out and remove such variables before doing a PCA, Especially when they describe actually (nearly) the same aspect of an issue. For instance, Tansmitted_Byte and Packet_Transmitted have a correlation of 1, because they reflect the same quantity up to a ratio Packet Size_Byte, which, as being mentioned here above, never changes. Thus, we will remove one of both. Which one to remove is of our free choice. Here, we consider that quantitative variables in packets may be more reader friendly than those in bytes in terms of unit, so that we keep the variable Packet_Transmitted and drop the other one. But what about the high correlation between other variables (e.g. higher than 97%) ? Shall we remove the nearly redundant variables too before doing our PCA? The statistical community doesn’t have a straightforward anwer to it. As a matter of fact, it hugely depends on the nature of data and the purpose to do the PCA. On one hand, like we said, highly correlated variables would be possible to strongly influence the result of the PCA and, as a result, the real contributions to the principal components of the underlying variables that are truely meaningful. If our PCA is meant to give such information, then high correlation should better be avoided prior to the PCA. On the other hand, however, a PCA with redundant variables can still faithfully reveal the high correlation between them, though principal components would be probably established otherwise. In that sense, if it is an exploratory PCA that we are doing, which only aims to find a broad outline of the relationships between variables disregarding how principal components are built, then including some redundant ones may be fine. In the light of this, we decide to go an onerous but careful way, in which we do firstly a PCA with almost all the variables. With both the correlation circle of PCA and the correlation heatmap, we then kick out the redundant variables and do a second PCA with only variables that we consider to be meaningful. Further analysis (variable and individual relationship, quantitative and qualitative variable relationship) shall also be based on the latter PCA. In a rough and rapid preprocessing procedure, we could limit our focus on high pairwise correlations (the reader should know that in a more rigorous treatment, high correlations within a multuple tuple of variables should also be considered) and refer to the heatmap of variable correlations. We may set a threshold, e.g. 0.97, and find out all couples whose absolute value of correlation exceeds this threshold, before we remove one of both variables by verifying that they are indeed telling (nearly) the same story.
library("factoextra")
pcaOBS <- prcomp(OBScomplet[! names(OBScomplet) %in% c("Node.Status", "Class")], scale. = TRUE, rank. = 2)
# fviz_eig(pcaOBS)
summary(pcaOBS)$importance[3, c(1, 2)]## PC1 PC2
## 0.52732 0.79172fviz_pca_var(pcaOBS, col.var = "contrib", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE)## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## Warning in var.loadings * comp.sdev: 长的对象长度不是短的对象长度的整倍数
## We see that in the correlation circle there are four subgroups of very closely situated variables which are potentially
## redundant variables (visibly there are five, but the one at the very left is highly negatively correlated with the one at the
## very right). For example, Tansmitted_Byte`, `Packet_Transmitted` and `Full_Bandwidth` are even perfectly correlated,
## which can be also confirmed by the previous correlation heatmap. No doubt those subgroups consist of the most contributing
## variables, because they are redundant! We now decide to remove extremely high correlation among variables (greater than
## 97) for our next PCA so that only
## one variable of each of the four subgroups should stay in the game. Another reason for doing this, in a point of view
## of field knowledge, is that all the variables
## within the same subgroup mean in fact the same thing just in some different way. At the end, we choose to keep
## `Packet.Received..Rate`, `Packet_Received`, `Packet_Transmitted` and `Packet_Lost` as representatives of their belonging subgroup along with
## other well defined variables. In the more balanced coming PCA with uniquely the non redundqnt variables, we could spot
## a change in variance contributions.
pcaOBS2 <- prcomp(OBScomplet[c("Packet.Received..Rate", "Packet_Received", "Packet_Transmitted", "Packet_lost",
"Average_Delay_Time_Per_Sec", "X10.Run.Delay", "Node", "Received_Byte", "Flood.Status")], scale. = TRUE, rank. = 3)
summary(pcaOBS2)$importance[3, c(1, 2, 3)]## PC1 PC2 PC3
## 0.36840 0.61203 0.75056fviz_eig(pcaOBS, ncp = 3, addlabels = TRUE, ylim = c(0, 60))
fviz_pca_var(pcaOBS2, col.var = "contrib", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE)
## Following information can be extracted from the correlation circle of PCA above:
## `Flood.Status`, `Packet_lost`, `Packet_Transmitted`, `Packet_Received` and `Packet.Received..Rate` are the five most well
## represented or in other words most contributing variables to the first both principal dimensions.
## `Packet_Received` has no contribution to the first dimension while `Node` has no contribution to the second one.
## `Received_Byte` has little contribution to the first dimension while `Packe_lost` has litte contribution to the second one.
## `X10.Run.Delay` and Àverage_Delay_Time_Per_Sec` seem to be correlated in the projected dataset onto the first two dimensions.
## `Packet.Received..Rate` and `Flood.Status` are highly negatively correlated.
## To extract all information about the variables, we can do
variables <- get_pca_var(pcaOBS2)
## What are the coordinates of the variables selected?
# dim(variables$coord) # 9, 9
# head(variables$coord)
variables$coord[, 1:3]## Dim.1 Dim.2 Dim.3
## Packet.Received..Rate -0.7598709053 0.600722370 -0.1033570
## Packet_Received -0.9172582980 0.001244397 0.2268809
## Packet_Transmitted -0.7944946606 -0.430210811 0.3630639
## Packet_lost -0.1315211178 -0.886093952 0.3516166
## Average_Delay_Time_Per_Sec 0.5366453995 0.398986327 0.6148888
## X10.Run.Delay 0.3971744367 0.532528682 0.5054290
## Node 0.0003522424 0.248589468 0.4157637
## Received_Byte -0.5772036435 0.030542401 0.3098019
## Flood.Status 0.6851099789 -0.596702315 0.1637975## What is the quality of representation of the variables by the first two components?
variables$cos2[, 1:2]## Dim.1 Dim.2
## Packet.Received..Rate 5.774038e-01 3.608674e-01
## Packet_Received 8.413628e-01 1.548523e-06
## Packet_Transmitted 6.312218e-01 1.850813e-01
## Packet_lost 1.729780e-02 7.851625e-01
## Average_Delay_Time_Per_Sec 2.879883e-01 1.591901e-01
## X10.Run.Delay 1.577475e-01 2.835868e-01
## Node 1.240747e-07 6.179672e-02
## Received_Byte 3.331640e-01 9.328383e-04
## Flood.Status 4.693757e-01 3.560537e-01library("corrplot")## Warning: package 'corrplot' was built under R version 3.4.3## corrplot 0.84 loadedcorrplot(variables$cos2[, 1:2], is.corr=FALSE)
## Total representation quality on dimension 1 and 2
fviz_cos2(pcaOBS2, choice = "var", axes = 1:2)
## How the the contribution of the variables to the first two components?
variables$contrib[, 1:2]## Dim.1 Dim.2
## Packet.Received..Rate 1.741496e+01 1.645788e+01
## Packet_Received 2.537618e+01 7.062263e-05
## Packet_Transmitted 1.903815e+01 8.440901e+00
## Packet_lost 5.217156e-01 3.580847e+01
## Average_Delay_Time_Per_Sec 8.685957e+00 7.260093e+00
## X10.Run.Delay 4.757792e+00 1.293338e+01
## Node 3.742192e-06 2.818328e+00
## Received_Byte 1.004849e+01 4.254343e-02
## Flood.Status 1.415675e+01 1.623834e+01corrplot(variables$contrib[, 1:2], is.corr=FALSE)
## Contribution of variables to PC1
fviz_contrib(pcaOBS2, choice = "var", axes = 1)
## Contribution of variables to PC2
fviz_contrib(pcaOBS2, choice = "var", axes = 2)
### Now we would like to plot some individuals. We can see that here, using redundant variables in the PCA or not will
### lead to a considerable difference.
## Firstly a graph of 20 randomly selected individuals drawn in the PCA with redundant variables, coloured by their quality of
## representation
fviz_pca_ind(pcaOBS, col.ind = "cos2", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE,
select.ind = list(name = sample.int(n = nrow(OBS), size = 20)))
## Their quality of representation is always the best, equal to 1! This is due to the fact that the first dimension
## consist of a huge amount of redundant information, so that an individual can be easily well represented by
## only these variables of him.
## Then we show a graph of 20 randomly selected individuals drawn in the PCA _without_ redundant variables, coloured by their quality of
## representation
fviz_pca_ind(pcaOBS2, col.ind = "cos2", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE,
select.ind = list(name = sample.int(n = nrow(OBS), size = 20)))
## All kinds of quality can be observed this time, which is more meaningful than in the previous case. Hence, this PCA is what
## we are going to keep using in the rest of our analysis.
fviz_pca_ind(pcaOBS2, col.ind = "cos2", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"), repel = TRUE,
select.ind = list(name = sample.int(n = nrow(OBS), size = 20)))
## We now try to involve the categorical information: `Node.Status` and `Class`.
## Firstly a graph of some randomly selected individuals coloured by subgroups of `Node.Status`
fviz_pca_ind(pcaOBS2, geom = "point", habillage = OBS$Node.Status, palette = "jco",
addEllipses = FALSE, legend.title = "Node Status")
## Then a graph of randomly selected individuals coloured by subgroups of `Node.Status`
fviz_pca_ind(pcaOBS2, geom = "point", habillage = OBS$Class, palette = "RdBu",
select.ind = list(name = 1:1075), legend.title = "Class")
## Now we draw some biplots with randomly selected individuals and variables
library(gridExtra)## Warning: package 'gridExtra' was built under R version 3.4.3plot1 <- fviz_pca_biplot(pcaOBS2,
habillage = OBS$Node.Status, palette = "jco",
addEllipses = FALSE, label = "var",
col.var = "darkgreen", repel = TRUE, title = NULL,
legend.title = "Node Status",
subtitle = "Coloured by Node Status", xlab = "PC1", ylab = "PC2")
plot2 <- fviz_pca_biplot(pcaOBS2,
habillage = OBS$Class, palette = "RdBu",
addEllipses = FALSE, label = "var",
col.var = "darkgreen", repel = TRUE,
legend.title = "Class", title = NULL,
subtitle = "Coloured by Class", xlab = "PC1", ylab = "PC2")
grid.arrange(plot1, plot2, ncol=2, top = "Randomly selected individuals with meaningful variables")
library(FactoMineR)
#### Attention: On ne peut pas faire le graphe de quanti et quali ensemble! Car elles ne partagent pas les me;es coordonnees.
#### Par contre quali et individus ensemble c'est possible mais ca revient a sous-groupes avec ellipse.
#### Pour tracer quali et quanti ensemble, il faut absolument passer par FAMD.
pcaOBS3 <- PCA(cbind(OBScomplet[c("Packet.Received..Rate", "Packet_Received", "Packet_Transmitted", "Packet_lost",
"Average_Delay_Time_Per_Sec", "X10.Run.Delay", "Node", "Received_Byte", "Flood.Status")],
OBS[c("Node.Status", "Class")]), quali.sup = 10:11, graph = FALSE)
p <- fviz_pca_var(pcaOBS3)
fviz_add(p, pcaOBS3$quali.sup$coord, color = "red")
famdOBS <- FAMD(cbind(OBScomplet[c("Packet.Received..Rate", "Packet_Received", "Packet_Transmitted", "Packet_lost",
"Average_Delay_Time_Per_Sec", "X10.Run.Delay", "Node", "Received_Byte", "Flood.Status")],
OBS[c("Node.Status", "Class")]), graph = FALSE)
cumsum(famdOBS$eig[, 2])## [1] 32.76325 51.12368 62.28384 71.62478 78.49738plot(famdOBS, choix = "var")